Then Theorem REF  reduces to Theorem 5.2 of Song et al. [1]}, the global maximum principle of completely observed case for SDEPs with the following relation
\(\begin{aligned}&(m,n^1,\tilde{n}^1)=(p,q,k),\\&(\tilde{P},Q^1,\tilde{Q}^1)=(P,Q,K),\end{aligned}\) 
